This study introduces a new type of supply contract, the quadratic quantity discount contract, whose average transfer payment is a quadratic function. Thus, both the total and average quantity discounts increase nonlinearly in order quantity, unlike the typical linear quantity discount contract, whose total discount is nonlinear but average payment is a linear function of order quantity. We reveal the quadratic quantity discount contract’s unique properties by comparing it with linear quantity discount and wholesale price contracts. Our investigation, conducted in basic and closed-loop supply chain situations, reveals the potential of the quadratic quantity discount contract to be considered a serious choice for supply chain managers in various situations. Specifically, we reveal that the quadratic quantity discount contract always coordinates the supply chain, achieving the first-best supply chain profit while always enhancing the profits of all players. This is the most important difference from the typical linear quantity discount contract that entails a profit distribution problem and bargaining power issues. Further, unlike other contracts, its profit improvement performance is predictable; moreover, it offers the acceptable wholesale price with an additional nonlinear average discount. However, when the supplier can exercise its power and only considers its own profit, the typical linear quantity discount contract can be considered the better option, as it produces superior profits for the supplier, but the profits of the retailer and supply chain are sacrificed in this case. If the supplier considers the supply chain’s long-term health and wants voluntary compliance from other players, the quadratic quantity discount contract is the optimal choice.

本研究引入了一种新型的供应合同，即二次数量折扣合同，其平均转移支付是一个二次函数。因此，总折扣和平均数量折扣都随订单数量非线性增加，这与典型的线性数量折扣合同不同，后者的总折扣是非线性的，但平均付款是订单数量的线性函数。我们通过与线性数量折扣和批发价格合同的比较，揭示了二次数量折扣合同的独特性质。我们在基本和闭环供应链情况下进行的调查揭示了二次数量折扣合同在各种情况下被视为供应链经理的严肃选择的潜力。具体来说，我们揭示了二次数量折扣合约始终协调供应链，在始终提高所有参与者的利润的同时实现供应链利润第一。这是与典型的线性数量折扣合同最重要的区别，后者涉及利润分配问题和议价能力问题。此外，与其他合同不同，其利润提升表现是可预测的；此外，它提供了可接受的批发价格和额外的非线性平均折扣。但是，当供应商可以行使权力而只考虑自己的利润时，典型的线性数量折扣合同可以被认为是更好的选择，因为它为供应商产生了超额利润，但牺牲了零售商和供应链的利润。这个案例。